A-level · Probability

Calculating probabilities and sample spaceExam-style questions

Probability as the proportion of equally likely outcomes that are favourable; listing the sample space (including for two dice and two-way tables); the fact that probabilities of all outcomes sum to 1, and the complement rule P(A′) = 1 − P(A); and the difference between theoretical probability and experimental (relative frequency) probability.

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7 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
Two fair dice are rolled. Find the probability of getting at least one six.
Level 3 · 2 marksTry it
2
A card is drawn at random from a standard pack of $52$ . Find the probability that it is a king or a heart.
Level 3 · 2 marksTry it
3
Of $100$ people, $60$ are male and $40$ female; $30$ of the males and $15$ of the females wear glasses. A person is chosen at random.
(a) Find $P(\text{wears glasses})$ .
(b) Find $P(\text{female and wears glasses})$ .
Level 3 · 2 marksTry it
4
A biased die lands on a six with probability $0.2$ . It is rolled three times. Find the probability of at least one six, to 3 d.p.
Level 3 · 2 marksTry it
5
Two fair dice are rolled. Find the probability that the product of the scores is greater than $20$ .
Level 3 · 2 marksTry it